Question

A box contains $90$ disc which are numbered from $1$ to $90$. If one disc is drawn at random from the box, find the probability that the number on the disc is (i) a two-digit number (ii) a perfect square (iii) a number is divisible by $7$.

Answer 1

$i)$ Number of two-digit number $=90-9=81$, Total number $=90$

Probability of being a two-digit number $=\frac{81}{90}$

$ii)$Since there are $9$ perfect square numbers such that $1,4,9,16,25,36,49,64,81$

Probability of being a perfect square $=\frac{9}{90}=\frac{1}{10}$

$iii)$ Since there are $12$ numbers divisible of $7$ such that $7,14,21,28,35,42,49,56,63,70,77,84$

Probability of being a perfect square $=\frac{12}{90}=\frac{2}{15}$.